A few lucky ones discovered they were able to stay on the job for at least a few more days.

Workers who work at Housing and Urban Development, the Internal Revenue Service and a handful of other agencies went to the office for up to four hours to help shut down their offices.

"It was definitely rush, rush, rush," said Pete Randazzo, president of civilian workers at the Naval Postgraduate School in Monterrey, Calif., who was among 1,500 workers on furlough at the school. "Everything was last-minute."

A senior Pentagon official told CNN that the new law may keep more civilian workers on the job if they support active duty military personnel.

"Our lawyers believe that maybe we can expand the exempt status," said Defense Secretary Chuck Hagel on Tuesday.

At the Texas Red River Army Depot, which refurbishes military vehicles, most of the 2,300 civilian workers learned Tuesday that they would continue to stay on the job and get paid. Only about 14 workers were furloughed, said Cebron O'Bier, president of the union at the depot. Many of the same employees were also furloughed during sequester earlier this year.

However, it was unclear how long their jobs could be saved.

"As of right now, we're still working, but it's on a day-by-day, hour-to-hour basis," O'Bier said.

Workers at the Department of Energy have also averted furloughs for now because the agency's operating budget comes from previous years' funding.

However, an official warned that if the shutdown lasts beyond a "short period of time," the agency would resort to furloughs of "nonessential operations, resulting in employee and contractor furloughs."

Similarly, the federal courts stockpiled enough 2013 funds to remain fully open for at least the first 10 days of the shutdown.

Hundreds of workers at the Centers for Medicare & Medicaid Services were disappointed to discover that despite playing a key role in administering Obamacare -- the expanded health care coverage that kicked in on Tuesday -- they'd be stuck at home on furlough.

"It's such an interesting day for us, because a lot of us were very involved in preparing for the launch day," said one worker for the Centers for Medicare & Medicaid Services who wasn't authorized to speak on the record.

"It would have been nice to be part of the history of the opening of the marketplace. But given all the trainings we've been through, a half day breather is not the worst thing in the world. We just hope we'll get paid."

Meanwhile, hundreds of workers at the Federal Aviation Administration were told to start shutting down their offices late Monday. But workers were not given specific instructions, like whether they could apply for unemployment insurance, said researcher Karen Buondonno, who is with the local National Federation of Federal Employees union.

"We had extremely minimal information when we left," said Buondonno, who has been furloughed three times in two years. "The (furlough) stress is causing a lot of anxiety. We're not air traffic controllers, but we do affect the future of aviation and it's really hard to get our job done."